Exploration on dynamics in a discrete predator-prey competitive model involving feedback controls

In this work, we set up a new discrete predator-prey competitive model with time-varying delays and feedback controls. By virtue of the difference inequality knowledge, a sufficient condition which guarantees the permanence of the established discrete predator-prey competitive model with time-varying delays and feedback controls is derived. Under some appropriate parameter conditions, we have proved that the periodic solution of the system without delay exists and globally attractive. To verify the correctness of the derived theoretical fruits, we give two examples and execute computer simulations. Our obtained results are novel and complement previous known results.

Automated summary

In this work, a new discrete predator-prey competitive model with time-varying delays and feedback controls is established. A sufficient condition for the permanence of the model is derived using difference inequality knowledge. It is proven that the system has a periodic solution without delay under certain parameter conditions and is globally attractive. Two examples and computer simulations are provided to validate the theoretical results, which are novel and complement previous findings.